Two people fall madly in love and think no one notices, because they see only each other. But the heat of their heedless erotic glow is bound to attract attention; it singes onlookers, upends the natural order of propriety, sets tongues to wagging — especially if the young man is a dashing Russian soldier, and the lady in question is married to a revered government official and the mother of a child she adores. So nakedly operatic is the passion of Count Vronsky and Anna Karenina, they may as well be doing it on stage.

In the intelligently ecstatic new adaptation of Anna Karenina adaptation written by Tom Stoppard and directed by Joe Wright, all the world’s a stage — a 19th-century theater whose ornate confines are the setting for scenes taking place in Anna’s home town of St. Petersburg and in the social and political center of Moscow. Steeplechase horses gallop across the boards; a quiet dinner or a military banquet may be staged there. And when Anna (Keira Knightley) and Vronsky (Aaron Taylor-Johnson) meet, the theatrical intensity of their first moments in each other’s arms makes those around them not fellow performers but mute spectators, awed and aghast.

Leo Tolstoy’s 1877 novel, which generations of schoolchildren and moviegoers know as the story of the woman who threw herself under a train for love, fulfills Friedrich Schiller’s definition of adulterous love as a “bourgeois tragedy.” Tragedy for the woman, of course; men could survive a tryst with no damage to their reputations. For eight years, Anna has pursued marriage with Judge Alexei Karenin (righteous, balding Jude Law), for whom she feels respect; her love is poured into their beautiful son Seryozha (Oskar McNamara). A more worldly woman, the countess Vronskaya (Olivia Williams), counsels Anna to follow her erotic intuitions, saying, “I’d rather end up wishing I hadn’t than wishing I had, wouldn’t you?” The countess’s seraphic blond son, Alexei Vronsky, will test that thesis by becoming the object of Anna’s obsessions. Knowing she will be ostracized by the society she was born into, Anna plunges into the affair.

Wright’s strategy of setting most of the action on a stage (his idea, not Stoppard’s) takes some getting used to. In early scenes, the headlong bustle of Seamus McGarvey’s camera and the arch playing of the actors, many of them rendering comic judgments by sucking in their cheeks, prime the spectator to expect that this will be an Anna reduced to opera buffo. The pace continues furious, but the characters soon find a home in this bold new structure — one ornamented by Dario Marianelli’s luscious score. In a way this is opera, but grand opera, with the emotions running at fever pitch and the actors as likely to dance (choreography by Sidi Larbi Cherkaoui) as walk. Vronsky’s and Anna’s meeting at a formal ball expresses their love through dance, exactly as the classic routines of Fred Astaire and Ginger Rogers did in their ’30s musicals. As Vronsky and Anna whirl, the other dancers freeze. Everyone can detect the expert passion in their movements; the couple might have been spotted in the act of love.

In tone less Russian, or British, than Italian, Wright’s Anna Karenina has crucial links to Luchino Visconti’s 1954 Senso, in which a woman of title (the great Alida Valli) risks her marriage, her standing and her pride on an affair with a selfish young officer (Farley Granger). It also pulses with a hothouse brio worthy of Federico Fellini, until the Tolstoy tale morphs into a kind of Leo Dolce Vita — for this Anna is a modern parable of the instant scandal passion can stoke. The members of White Russian high society need no texts or Tweets to spread news of a princess’s adulterous affair; catty whispers and raised eyebrows will convey the message nicely. When every intimacy is made public, Anna and Vronsky’s secret ardor is a form of exhibitionism.

The novel has been filmed at least two dozen times, including silent and sound-movie versions, in 1927 and 1935, with Greta Garbo, and a 1948 film with Vivien Leigh. Two of the most incandescent stars of Hollywood’s Golden Age would be tough competition for Knightley, if she were playing the same kind of Anna. But guided by Wright, her director for Pride and Prejudice and Atonement, Knightley embodies Anna as a girlish woman who has never felt erotic love; once smitten, she is raised to heavenly ecstasy before tumbling into the abyss of shame. It’s a nervy performance, acutely attuned to the volcanic changes a naive creature must enjoy and endure on her first leap into mad passion. She helps make Anna Karenina an operatic romance worth singing about.